A brushless motor used in an electric power steering apparatus, etc., is controlled by supplying an electric current to a stator coil in accordance with a rotation angle of a rotor. There is thus known a rotation angle detection device that uses a detection rotor that rotates in accordance with rotation of the brushless motor to detect the rotation angle of the rotor of the brushless motor. Specifically, as shown in FIG. 10, a detection rotor 101 (hereinafter referred to as the “rotor 101”) includes a cylindrical magnet 102 having a plurality of magnetic pole pairs corresponding to magnetic pole pairs provided in a rotor of a brushless motor. At a periphery of the rotor 101, two magnetic sensors 121 and 122 are disposed at a predetermined angular interval centered at a central rotation axis of the rotor 101. Sinusoidal signals with a predetermined phase difference are output from the respective magnetic sensors 121 and 122. The rotation angle of the rotor 101 (rotation angle of the rotor of the brushless motor) is detected based on the two sinusoidal signals.
In the present example, the magnet 102 has five magnetic pole pairs. That is, the magnet 102 has ten magnetic poles disposed at equiangular intervals. Each magnetic pole is disposed at an angular interval of 36° (180° as electrical angle) centered at the central rotation axis of the rotor 101. Also, the two magnetic sensors 121 and 122 are disposed at an angular interval of 18° (90° as electrical angle) centered at the central rotation axis of the rotor 101.
A direction indicated by an arrow in FIG. 10 shall be deemed to be a positive direction of rotation of the detection rotor 101. It shall also be deemed that the rotation angle of the rotor 101 increases when the rotor 101 is rotated in the positive direction, and the rotation angle of the rotor 101 decreases when the rotor 101 is rotated in the opposite direction. The sinusoidal signals V1 and V2, with each of which a single cycle is a period in which the rotor 101 rotates by an angle corresponding to a single magnetic pole pair (72° (360° as electrical angle)), are output from the respective magnetic sensors 121 and 122 as shown in FIG. 11.
Here, an absolute rotation angle of the rotor 101 from a predetermined reference position shall be deemed to be the absolute rotation angle (rotation angle in accordance with the mechanical angle) θA of the rotor 101. An angular range of a single rotation of the rotor 101 shall be divided into five divisions corresponding to the five magnetic pole pairs, and an angle of the rotor 101 with a start position of each division being expressed as 0° and an end position being expressed as 360° shall be deemed to be a relative rotation angle θR of the rotor 101. In the present case, the ten magnetic poles are equal in angular width and thus the relative rotation angle θR of the rotor 101 matches the electrical angle of the rotor of the brushless motor.
Here, it shall be deemed that the output signal V1=A1·sin θR is output from the first magnetic sensor 121 and the output signal V2=A2·cos θR is output from the second magnetic sensor 122. A1 and A2 are amplitudes. If the amplitudes A1 and A2 of the two output signals V1 and V2 are deemed to be equal, the relative rotation angle θR of the rotor 101 can be determined based on the following formula (1) using the two output signals V1 and V2.
                                                                        θ                R                            =                            ⁢                                                tan                                      -                    1                                                  ⁡                                  (                                      sin                    ⁢                                                                                  ⁢                                                                  θ                        R                                            /                      cos                                        ⁢                                                                                  ⁢                                          θ                      R                                                        )                                                                                                        =                            ⁢                                                tan                                      -                    1                                                  ⁡                                  (                                      V                    ⁢                                                                                  ⁢                                          1                      /                      V                                        ⁢                                                                                  ⁢                    2                                    )                                                                                        (        1        )            
The brushless motor is controlled using the relative rotation angle θR thus determined.
In a case where the absolute rotation angle θA of the rotor 101 is equal to a mechanical angle of the rotor 101 from a predetermined reference position, the absolute rotation angle θA of the rotor 101 can be determined based on, for example, the following formula (2) and using the relative rotation angle θR.θA={θR+360×(j−1)}/5(j=1,2, . . . 5)  (2)